Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 448

CHAPTER VII-MEASUREMENT OF AREAS.
251
through the sky and) met in the city there (between the hills); and it turned out that they had travelled (along the sky) over equal distances. (Under these circumstances), of what numerical value were the segments (of the basal line between the two hills)? Of what value, O you who know calculation, is the numerical measure of the equal distance travelled in this (area) representable by a (suspended) swing.
2084–2094. The height of one hill is 20 yõjanas ; and similarly, that of another (hill) is 24 yojanas. The intervening space between them is 22 yojanas (in length). Two mendicants, who stayed on the tops of these two hills, (one on each), and were able to move through the sky, came down, for the purpose of begging their food, to the city situated between those (two hills), and were found to have travelled (along the sky) over equal distances. What is the measure of the length) of the intervening space between that (city) in the middle and the hills (on either side).
The rule for arriving at the value of the number of days required for the meeting together of two persons moving with unequal speed along a course representable by (the boundary of) a triangle consisting of (three) unequal sides :
2101. The sum of the squares (of the numerical values) of the daily speeds (of the two men) is divided by the difference between the squares of the values of (those same) daily speeds. 'The quotient (so obtained) is multiplied by the number of days spent (hy ne of the men) in travelling northwards (before travelling to the south-east to meet the other man). The meeting together of these two men takes place at the end of the number of days measured by this product.
210$. The course contemplated here is that along the sides of a right angled triangle. The formula given in the rale, if algebraically represented, is
where æ is the number of days taken to go through the hypotenuse course, a and b the rates of journey of the two men, and d the number of days taken in going northwards. This follows from the under mentioned equation which in based on the data given in the problem:
6° 2° = 2 2 + (x+) x a?